Yes, a lot. You will probably see only 25% of the game if you only follow the story. Almost all sidequests are optional and some of them will be gone after reaching certain points in the story line! Check the walkthrough for more details. The quests are listed on the individual story line pages before they will be gone.

All monsters (maybe except The Fallen and The Lost who have a turn limit) can be defeated by simply levelling up - getting better stats, arts and equipment or using better formations. Physical attacks have a better AP/damage ratio against single targets so focus on those. Flanking or Rear Assaults help to keep the morale up. Also check the talk page of the monster in question, you may find additional tips there.

You can have up to 18 units in battle organized in up to 5 unions. On the XBOX you are limited to 6 active leaders; the remaining units can only be soldiers.

What are the effects of the "What should I focus on?"-questions asked by the leaders?Edit

Depending on the answer the leader will upgrade to different weapons and accessories.

Balanced results in average weapons and balanced stats. HP and AP/SPD bonus accessories are used. This route yields the highest HP.

Combat results in weapons with high physical attack and defence. STR and physical resistance bonus accessories are used.

Mystic results in weapons with high mystic attack and defence. The same accessories as balanced are used, it's unknown whether this is a bug or not.

It is recommended to answer both questions the same, as a mixture has unpredictable results. Also note that the arts used in combat have an impact too. If you mostly use Mystic Arts then even a Combat focused leader will change to Balanced or Mystic. Again, the result will be an unpredictable mixture or a complete change in focus. Lastly, you cannot reverse these changes.

All combat arts are learned by using a matching weapon. Keep using the regular attack, they will learn the lowest art after some time.

Mystic and item arts are different. For Rush you have to get certain special items to learn it, so check his page for more details. All other units have a fixed list of skills they can learn at specific BR levels. Once the appropriate BR level is reached, use the character in at least one battle, and upon exiting to the world map or a town they will ask you if they should learn the new skill type.

To go beyond the first art, simply keep using it. After a certain amount of uses it will upgrade to higher tiers and you will learn the higher level arts.

If a leader asks to learn a certain skill and I decline, will they ask again later?Edit

No, you have only one chance to learn the new skill. On the PC, there is very little consequence to letting them learn the skill as it can be toggled off if unneeded. On the X360, it's better to not let them learn any skills unless it is a recovery skill (Remedies/Herbs/Lotions) and/or an offensive mystic skill if the unit has high Intellect and few attack options. Doing so will help limit the number of arts that unit will contribute to commands.